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Eight degrees of separation
 Research in Economics
, 2011
"... The paper presents a model of network formation where every connected couple give a contribution to the aggregate payoff, eventually discounted by their distance, and the resources are split between agents through the Myerson value. As equilibrium concept we adopt a refinement of pairwise stability. ..."
Abstract

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The paper presents a model of network formation where every connected couple give a contribution to the aggregate payoff, eventually discounted by their distance, and the resources are split between agents through the Myerson value. As equilibrium concept we adopt a refinement of pairwise stability. The only parameters are the number N of agents and a constant cost k for every agent to maintain any single link. This setup shows a wide multiplicity of equilibria, all of them connected, as k ranges over non trivial cases. We are able to show that, for any N, when the equilibrium is a tree (acyclical connected graph), which happens for high k, and there is no decay, the diameter of such a network never exceeds 8 (i.e. there are no two nodes with distance greater than 8). Adopting no decay and studying only trees, we facilitate the analysis but impose worstcase scenarios: we conjecture that the limit of 8 should apply for any possible nonempty equilibrium with